A capacitor of 10 micro Farad and an inductor of 1H are joined in series. An ac of 50Hz is applied to this combination. What is the impedance of the combination?

Hence $X_L=\omega L=2\pi /L=2\pi \times 50\times 1=100\pi \Omega$

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times 10\times {10}^{-6}}=\frac{{10}^3}{\pi }\Omega$

So, $X=X_L-X_C=100\pi -\frac{{10}^3}{\pi }={10}^2\left[\frac{{\pi }^2-10}{\pi }\right]\Omega$

$Z+\sqrt{R^2+X^2}=\left|X\right|={10}^2\left[\frac{10-9.86}{\pi }\right]\Omega$

i.e. $Z=\frac{14}{\pi }\Omega =4.47\Omega$